adjective 1. without the faculty of reason; deprived of reason. 2. without or deprived of normal mental clarity or sound judgment. 3. not in accordance with reason; utterly illogical: irrational arguments. 4. not endowed with the faculty of reason: irrational animals. 5. Mathematics.

6. Algebra. (of an equation) having an unknown under a radical sign or, alternately, with a fractional exponent. 7. Greek and Latin Prosody.

noun, Mathematics. 1. a number that cannot be exactly expressed as a ratio of two integers. noun 1. any real number that cannot be expressed as the ratio of two integers, such as π irrational number (ĭ-rāsh’ə-nəl) A number that cannot be expressed as a ratio between two integers and is not an imaginary number. […]

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